Bunuel wrote:
You make a new sequence by removing 2 elements from the sequence {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}. What is the standard deviation of the new sequence?
(1) The median of the new sequence is 10.
(2) The new sequence has the same average as the original sequence.
Note that we never need to use a standard deviation formula. We just need to understand that it's a measure of how spread out the values are from the average.
For example: {1, 3, 5} has a higher standard deviation than {2, 3, 4}, even though both sequences have the same average and median.
Statement 1:This means that we would remove one value above 10, and one value below 10.
If we removed the most extreme values, 1 and 19, the standard deviation would be lower (values are less spread out) than if we removed the values closest to the average, 9 and 11.
So, different standard deviations are possible.
Insufficient.Statement 2:Since this is an evenly spaced set, the average is equal to the median of 10. For the new average to stay the same, we would need to remove 2 values that are equidistant from the original average of 10. (such as 9 and 11, 7 and 13, 5 and 15, etc.)
So, we can use the same 2 cases that we used above:
If we removed the most extreme values, 1 and 19, the standard deviation would be lower (values are less spread out) than if we removed the values closest to the average, 9 and 11.
Insufficient.
Together:Since we already used the same 2 cases for statements 1 and 2, we don't have to test new numbers. When possible, this is a good habit to save time.
Insufficient, so our answer is E.